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Applied Math

In academia, mathematics is often divided into two distinct branches: pure and applied. Pure mathematics is a captivating field where mathematicians explore abstract ideas in areas such as number theory, algebra, analysis, combinatorics, logic, etc. The motivation for research tends to be more for the sake of expanding knowledge or for the joy of discovery. Though, there are plenty of applications in cryptography.

On the other hand, applied mathematics serves as a potent and practical toolset, utilizing mathematical tools to address real-world problems effectively. Professionals in my field frequently engage in collaborations with scientists, engineers, and economists, working together to confront open-ended problems. In most instances, our responsibilities involve constructing models, often in the form of systems of equations, to quantify some tangible situations. Then we use our expertise in numerical analysis and computation to derive practical solutions from these models.

The fundamental areas of applied math are real and complex analysis, differential equations, linear algebra and numerical analysis, so it is geared toward mathematical physics problems. But, when we work on specialized topics like: machine learning, signal processing, optimization, or control theory, we pick up new tools.